#111 InvertingaCoinTriangle

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Consider an equilateral triangle formed by closely packed pennies or other identical coins like the one shown in Figure 2.27. (The centers of the coins are assumed to be at the points of the equilateral triangular lattice.) Design an algorithm to flip the triangle upside down in the minimum number of moves if on each move you can slide one coin at a time to its new position. Give a compact formula for the number of minimum moves.